Question

The height of a triangle is 8 cm more than the base. If the area is 24 cm2, find the height and base of the triangle.

Answer 1

Answer:

height = 12 cm

base length = 4 cm

Step-by-step explanation:

area of a triangle

base length × height / 2

x = height

y = base length

x = y + 8

24 = y × (y + 8) / 2

48 = y × (y + 8) = y² + 8y

squared equation

y² + 8y - 48 = 0

solution

y = (-b ± sqrt(b² - 4ac))/(2a)

a = 1

b = 8

c = -48

y = (-8 ± sqrt(64 - 4×-48))/2 = (-8 ± sqrt(64 + 192))/2 =

= (-8 ± sqrt(256))/2 = (-8 ± 16)/2 = -4 ± 8

y1 = -4 + 8 = 4 cm

y2 = -4 - 8 = -12

but a negative base length did not make any sense, so only y = 4 remains.

x = y + 8 = 4 + 8 = 12 cm